Approximate the area under the graph of $f(x)=0.05 x^{4}-1.44 x^{2}+66$ over the interval $[1,9]$ by dividing the interval into 4 subintervals. Use the left endpoint of each subinterval.
The area under the graph of $f(x)=0.05 x^{4}-1.44 x^{2}+66$ over the interval $[1,9]$ is approximately (Simplify your answer. Type an integer or a decimal.)

Step 1 ：We are given the function \(f(x)=0.05 x^{4}-1.44 x^{2}+66\) and asked to approximate the area under the curve over the interval \([1,9]\) by dividing the interval into 4 subintervals and using the left endpoint of each subinterval. This is a problem of numerical integration, and the method described is the Left Riemann Sum.

Step 2 ：The Left Riemann Sum is calculated by dividing the interval into equal subintervals, and for each subinterval, we calculate the area of the rectangle whose height is the value of the function at the left endpoint of the subinterval. The sum of these areas gives an approximation of the total area under the curve.

Step 3 ：The width of each subinterval is given by \((b - a) / n\), where \(a\) and \(b\) are the endpoints of the interval and \(n\) is the number of subintervals. In this case, \(a = 1\), \(b = 9\), and \(n = 4\), so the width of each subinterval is \((9 - 1) / 4 = 2\).

Step 4 ：The left endpoints of the subintervals are \(1, 3, 5, 7\). We will evaluate the function at these points and multiply by the width of the subintervals to get the areas of the rectangles.

Step 5 ：The calculated area under the curve of the function \(f(x)=0.05 x^{4}-1.44 x^{2}+66\) over the interval \([1,9]\) using the Left Riemann Sum method with 4 subintervals is approximately 596.88.

Step 6 ：Final Answer: The approximate area under the graph of \(f(x)=0.05 x^{4}-1.44 x^{2}+66\) over the interval \([1,9]\) using the Left Riemann Sum method with 4 subintervals is \(\boxed{596.88}\).